Identifying Dynamic Genes with Generalized Estimating Equations in scLANE

University of Florida - Dept. of Biostatistics - Bacher Group

Introduction

In this vignette we’ll focus on one of the more complicated features of scLANE: the usage of GEE models to identify dynamic genes when cells are grouped by some subject identity. The robust variance estimation available in GEE models allows us to make decisions about which genes are actually dynamic over pseudotime / latent time while accounting for intra-subject correlations between observations. The downsides are that the benefits of GEE models can be a little more difficult to explain to collaborators, and they take a little bit longer than GLMs to estimate. A refresher on what GEEs are and why they’re useful can be found here.

Libraries

library(dplyr)      # data manipulation
library(scran)      # single cell tools 
library(scLANE)     # differential expression over pseudotime
library(scater)     # single cell tools 
library(slingshot)  # pseudotime estimation

Data

First we’ll load in the lung tumor data from Zilionis et al (2019), and subset to only include tumor neutrophils. The authors found 5 continuous tumor neutrophil subsets in their analysis, and we’re interested in determining which genes drive subset-to-subset differentiation. The data were collected from 7 different patients, and thus the usage of GEE models is warranted in order to properly estimate within-patient gene expression correlations. Lastly, we’ll subset the object to only include genes that are expressed in at least 5 cells.

lung <- scRNAseq::ZilionisLungData(which = "human", filter = TRUE)
lung <- lung[, stringr::str_detect(lung$`Major cell type`, "tNeutrophils")]
lung <- lung[which(rowSums(counts(lung) > 0) >= 5), ]

Preprocessing

First we’ll preprocess the data in the typical way. We see that the neutrophils fall into 5 clusters, and that there is one odd outlier group of cells near the top of the UMAP plot. In addition, there is a decent amount of intra- and inter-patient variability. The cluster labels are not solely reflective of the cell subtypes, and seem to be driven by both patient identity as well as cell subtype.

lung <- logNormCounts(lung)
var_decomp <- modelGeneVar(lung)
top2k_hvgs <- getTopHVGs(var_decomp, n = 2000)
lung <- runPCA(lung, subset_row = top2k_hvgs)
reducedDim(lung, "PCAsub") <- reducedDim(lung, "PCA")[, 1:10, drop = FALSE]
lung <- runUMAP(lung, dimred = "PCAsub", n_dimred = 1:10)
g <- buildSNNGraph(lung, use.dimred = "PCAsub", k = 20)
clusters <- igraph::cluster_louvain(graph = g)$membership
colLabels(lung) <- factor(clusters)
plotUMAP(lung, colour_by = "label")

plotUMAP(lung, colour_by = "Patient")

plotUMAP(lung, colour_by = "Minor subset")

Estimating Pseudotime

We’ll use slingshot to estimate a pseudotime value for each cell. In this case, we see only one pseudotime lineage.

scl_lineage <- getLineages(reducedDim(lung, "PCAsub"), clusterLabels = clusters)
scl_crv <- getCurves(scl_lineage)
scl_cell_weights <- slingCurveWeights(scl_crv)
scl_pt <- slingPseudotime(scl_crv)
pt_df <- as.data.frame(scl_pt) %>% 
         mutate(across(everything(), function(x) x / max(x, na.rm = TRUE)))

Running scLANE

Global Test

We’re going to run scLANE solely on the top 100 most highly variable genes. This is for both computational quickness & in order to get interesting results (highly variable \(\implies\) dynamic, usually), as this is a just a tutorial. Note that we need to provide a (sorted) vector of subject IDs as well as a working correlation structure. In this case we opt for the exchangeable (AKA compound symmetry) structure, as it stands to reason that within-subject cells will have similar correlations.

lung_counts <- as.matrix(t(lung@assays@data$counts))[, top2k_hvgs[1:100]]
gene_stats <- testDynamic(expr.mat = lung_counts, 
                          pt = pt_df, 
                          is.gee = TRUE, 
                          id.vec = lung$Patient, 
                          cor.structure = "exchangeable", 
                          n.potential.basis.fns = 4, 
                          parallel.exec = TRUE, 
                          n.cores = 6, 
                          track.time = TRUE)

[1] "testDynamic evaluated 100 genes with 2 lineages apiece in 1.727 hours"

Let’s check out the results of the global differential expression test.

getResultsDE(gene_stats) %>% 
  select(-contains("LogLik"), -contains("Dev")) %>%  # not relevant to GEEs
  arrange(Gene, Lineage) %>% 
  slice_head(n = 10) %>% 
  kableExtra::kbl(digits = 5, 
                  align = "c", 
                  booktabs = TRUE, 
                  caption = "Lineage-level dynamic test", 
                  col.names = c("Gene", "Lineage", "Test Stat.", "P-value", "Test Stat. Type", "Test Notes", 
                                "Model Status", "Adj. P-value", "Gene Dynamic over Lineage", "Gene Dynamic")) %>% 
  kableExtra::kable_paper("hover", full_width = FALSE)

Lineage-level dynamic test

Gene	Lineage	Test Stat.	P-value	Test Stat. Type	Test Notes	Model Status	Adj. P-value	Gene Dynamic over Lineage	Gene Dynamic
AC245128.3	A	NA	NA	Wald	NA	MARGE model error, null model OK	NA	0	1
AC245128.3	B	14317.49413	0.00000	Wald	NA	MARGE model OK, null model OK	0.0000	1	1
ACSL1	A	NA	NA	Wald	NA	MARGE model error, null model OK	NA	0	0
ACSL1	B	15.06179	0.00176	Wald	NA	MARGE model OK, null model OK	0.3088	0	0
ACTB	A	1830.90455	0.00000	Wald	NA	MARGE model OK, null model OK	0.0000	1	1
ACTB	B	816.06553	0.00000	Wald	NA	MARGE model OK, null model OK	0.0000	1	1
ACTG1	A	NA	NA	Wald	NA	MARGE model error, null model OK	NA	0	0
ACTG1	B	8.46577	0.01451	Wald	NA	MARGE model OK, null model OK	1.0000	0	0
ADM	A	230.24808	0.00000	Wald	NA	MARGE model OK, null model OK	0.0000	1	1
ADM	B	826.35930	0.00000	Wald	NA	MARGE model OK, null model OK	0.0000	1	1

Slope Test

Next we can run the slope test to identify over which pseudotime intervals gene expression changes significantly.

testSlope(test.dyn.results = gene_stats) %>% 
  slice_head(n = 10) %>% 
  kableExtra::kbl(digits = 5, 
                  align = "c", 
                  booktabs = TRUE, 
                  caption = "Slope-level dynamic test", 
                  col.names = c("Gene", "Lineage", "Breakpoint", "Rounded Breakpoint", 
                                "Direction", "P-value", "Notes", "Adj. P-value", 
                                "Gene Dynamic over Lineage-Slope", "Gene Dynamic over Lineage", 
                                "Gene Dynamic")) %>% 
  kableExtra::kable_paper("hover", full_width = FALSE)

Slope-level dynamic test

Gene	Lineage	Breakpoint	Rounded Breakpoint	Direction	P-value	Notes	Adj. P-value	Gene Dynamic over Lineage-Slope	Gene Dynamic over Lineage	Gene Dynamic
AC245128.3	B	0.02320	0.0232	Right	0.00061	NA	0.16273	0	0	0
AC245128.3	1	NA	NA	NA	NA	MARGE model error, null model OK	NA	0	0	0
ACSL1	B	0.02320	0.0232	Right	0.00136	NA	0.36125	0	0	0
ACSL1	B	0.75149	0.7515	Right	0.00012	NA	0.03160	0	0	0
ACSL1	1	NA	NA	NA	NA	MARGE model error, null model OK	NA	0	0	0
ACTB	B	0.02320	0.0232	Right	0.05586	NA	1.00000	0	0	1
ACTB	A	0.37023	0.3702	Right	0.00000	NA	0.00000	1	1	1
ACTB	A	0.37314	0.3731	Left	0.00000	NA	0.00000	1	1	1
ACTG1	B	0.02320	0.0232	Right	0.00552	NA	1.00000	0	0	0
ACTG1	1	NA	NA	NA	NA	MARGE model error, null model OK	NA	0	0	0

Model Visualization

Lastly, we can plot the fitted models for a couple of the genes. In addition to the null (intercept-only) and MARGE models we can also compare to a GEE GLM with pseudotime as a covariate.

plotModels(test.dyn.res = gene_stats, 
           gene = "CXCL8", 
           pt = pt_df, 
           gene.counts = lung_counts, 
           is.gee = TRUE, 
           id.vec = lung$Patient, 
           cor.structure = "exchangeable")

plotModels(test.dyn.res = gene_stats, 
           gene = "RGS2", 
           pt = pt_df, 
           gene.counts = lung_counts, 
           is.gee = TRUE, 
           id.vec = lung$Patient, 
           cor.structure = "exchangeable")

Gene-level Analysis

Let’s cluster the genes based on their fitted values using hierarchical clustering with Ward’s linkage.

purrr::map(gene_stats, function(x) {
  if (stringr::str_detect(x$Lineage_A$Model_Status, "error")) {
    NA
  } else {
    x$Lineage_A$MARGE_Preds$marge_link_fit
  }
}) %>% 
  purrr::reduce(cbind) %>% 
  set_colnames(names(gene_stats)) %>% 
  #set_rownames(rownames(lung_counts)) %>% 
  janitor::remove_empty(which = "cols") -> fitted_vals
fitted_vals_pca <- prcomp(t(fitted_vals), center = TRUE, rank. = 10)$x
fitted_vals_clusts <- hclust(dist(fitted_vals_pca), method = "ward.D2")
ggdendro::ggdendrogram(fitted_vals_clusts) + 
  labs(title = "Heirarchical Clustering of Highly-Variable Genes") + 
  theme_classic(base_size = 14) + 
  theme(axis.text.x = element_text(angle = 90, size = 8), 
        plot.title = element_text(hjust = 0.5), 
        axis.text.y = element_blank(), 
        axis.title = element_blank())

Session Info

sessioninfo::session_info()

─ Session info ───────────────────────────────────────────────────────────────
 setting  value                       
 version  R version 4.0.4 (2021-02-15)
 os       macOS Big Sur 10.16         
 system   x86_64, darwin17.0          
 ui       X11                         
 language (EN)                        
 collate  en_US.UTF-8                 
 ctype    en_US.UTF-8                 
 tz       America/New_York            
 date     2022-05-08                  

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[1] /Library/Frameworks/R.framework/Versions/4.0/Resources/library